You can add groups to the side menu via the groups widget, however it is not by participation. It just lists however many groups you want to list there i believe. 

Dave

Dave, Hi.

I could not do what you said, I did not find this option in group settings. What I want is to list the groups a user participates in the space shown in the print.

I am not sure what theme that is you are using however what i am referring to is on the main page.  I have changed to the Darklets theme on my test site to make it more apparent to you.  This is on the left side bar and you can access the options by clicking on customize this page button.   Hope that helps :)

Hi, Dave, at the location you indicated I could put, I want is to have this option in the side of the system menu. Do you know if this is possible?

Not that i am aware of, i do not believe it is possible without custom coding.  

Okay Dave, thanks.